Stabilization of chaos-an algebraic theory

Summary form only given. A general problem statement can be stated as follows: given a (nonlinear) plant p, the problem is to find a (nonlinear) compensator c so that the overall system s is ´good´, in the sense that no chaotic motion can be generated. More specifically, let G be the set of all n-input n-output (nonlinear) operators, H be the subset of G in which no chaotic motion can be produced. Now the control problem can be stated more precisely as follows: given p epsilon G, find c epsilon G so that s epsilon H. The general problem is far too difficult to be solved. However, two general results can be presented. These results are in the form of two theorems which both depend on an important property that H can be characterized by systems in which almost periodical inputs produce almost periodical outputs.<>